The Strangest Macro Model Ever

I think that I usually understand what Paul Krugman is saying, even when I disagree with him. However, I do not think that I understand Why Inflation Targets Need to be Higher well enough to say whether or not I agree with him.

What I think he is saying is that the Phillips Curve constrains the ability of the Fed to set a credible inflation target. So, if the Fed says, "We are going to aim for 2 percent inflation," the market is going to say, "Sorry, but that will only raise aggregate demand enough to get you to 6 percent unemployment, which won't get you to 2 percent inflation (because of the aforementioned Phillips Curve). Therefore, we don't believe you, and so we won't let inflation go up at all."

On the other hand, if the Fed says, "We are going to aim for 3 percent inflation," the market is going to say, "That works," and inflation will go up.

So you get this discontinuity. If we have 0 inflation now, the Fed can credibly commit to 3 percent inflation, but not to 2 percent inflation. Anywhere between 0 inflation and 3 percent inflation is "no man's land" in this model.

I may be misinterpreting this. But if I am not misinterpreting it, I think that "no man's land" is too strange to be true. I don't buy these sort of discontinuities. If Krugman wants to say that the Fed cannot credibly commit to raise inflation at all, he can try telling that story (really pushing the Phillips Curve and a liquidity trap, I suppose). But, generally speaking, economic models with discontinuities of this sort are artifacts of strange assumptions, not reasonable descriptions of the real world.

I am willing to believe that the world is nonlinear. I can see where it would be hard to keep inflation steady at 5 to 10 percent, because I think that money demand becomes more unstable at that point, with the incentives kicking in for financial innovation to economize on the use of money. But that is a completely different story, and it does not create a "no man's land."

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Krugman is using the old threshold argument that I see many monetarists use. They believe that money operates like a nerve cell with a threshold for firing. If the stimulus to the nerve is below the threshold, the nerve won't fire. Krugman believes that there is a threshold to money so that any amount of monetary pumping below the threshold had no effect at all, but monetary pumping above that threshold is totally effective. It's the same old excuse that Keynesians have used for the repeated failure of fiscal stimuli.

But there is no empirical or logical evidence for a threshold in the economy. The economy has nonlinear effects, but that is nothing like the threshold effect. Monetarists hold to the threshold effect because they have seen hyperinflation, so they know that monetary policy can cause high levels of inflation. They just don't have a clue as to why it doesn't work all of the time. Why, for example, is monetary policy sometimes like pushing on a string and other times like throwing gas on a fire?

The answer lies in the fact that monetarists take the quantity theory of money too mechanically. Yes, an increase in the money stock does tend to cause price increases, with a lag and with all other things being equal. But all other things are rarely equal. Depressions can overwhelm the quantity theory for a long time.

For the monetary theory to work, people must be willing to borrow and they aren't in a depression. And for an increase in money to create price inflation there must be a shortage of goods, which there isn't in a depression. So during a depression monetary pumping is as useless as tits on a boar.

But once the economy turns around, idle resources are used up and people begin to borrow again, the quantity theory will kick in with a vengeance. That's why bad economists think there is a threshold.

Wait a minute, wait a minute... Arnold "Inflation Regime" Kling is taking issue with discontinuities in Krugman's model?! How does that make sense? Didn't you identify your own discontinuity as being between 3.5 and 5.5 percent (8/29/2010)?

I don't entirely understand Krugman's post either, but I didn't invest a whole lot of time in it. I figured the simple point was that unemployment and inflation are simultaneously determined and that when we're not at full employment, economic slack prevents an inflationary policy from having an impact on price levels until it is substantially stronger. Maybe that's a misinterpretation.

That, I have to say, is substantially more of an explanation for his discontinuity than I can find in this post about your prefered discontinuity: http://econlog.econlib.org/archives/2010/08/megan_mcardles.html

One more Austrian insight about QE: inflation only happens when the federal government borrows and spends the money. When it doesn't, QE produces mostly asset inflation, not cpi inflation as the monetarist long for.

re RP Long: What's strange is that the first graph depicts an entirely different relationship than the second graph, even though they graph the same things. How did this man graduate high school?

So? What is the concern here? Supply and demand graphs depict different relationships too... and you use them together to find stable equilibria. In fact it's the ONLY way to find an equilibrium (stable or otherwise) in two-dimensional space - identify two different relationships and put them together.

You flippantly ask how Krugman graduate high school - I'm wondering how you graduated middle school. Don't linear systems and basic algebra come in even before your freshman year of high school?

re my own: "Don't linear systems and basic algebra come in even before your freshman year of high school?"

In fairness to you, RP Long, I suppose Krugman's graphs weren't exactly linear... but still! Give me a break! Two equations and two unknowns shouldn't be that big of an obstacle for someone commenting on economics to surmount.

What's strange about Krugman's argument is that although he says that a modest inflation target can't work, it does work elsewhere. For example, the UK has had an explicit inflation targeting regime since 1997. From 1997-2003 the target was 2.5%, and from 2003- present the target has been 2%. Precisely the figures that Krugman says are impossible.

Now arguably there are special structural factors in the US economy that make this impossible. But I'm sceptical. I'm particularly unconvinced by his claim:

But how do you get inflation? Only by having a full-employment economy.

fundamentalist -
Ironically enough, the 1970s were figured out at least as early as 1968, and that material has been covered several times on Krugman's blog. I don't think it makes that much sense to throw crude-Phillip's-curve accusations at him when he's working on the low-inflation end of the Phillip's curve. The accusation simply doesn't stick (and I would guess even Arnold would agree on that).

Daniel, the statement is still wrong, regardless of what you may think they "figured out" in 1968 or what you may determine from the Philips curve. We can have inflation without full employment.

The important thing to keep in mind about Krugman's curves is that they're hypothetical. He is trying to imagine why monetary policy works sometimes and why it doesn't work other times. We might interpret the first chart as referring to anticipated inflation and the lower one as referring to actual inflation. Otherwise, as Kling has pointed out, the charts simply don't make sense. If you take Krugman literally, then he is saying that inflation reduces unemployment except when it doesn't. Regardless, there still is no empirical or logical evidence for a threshold effect. It's all in Krugman's imagination.

RP Long: Why do you think these are supposed to be just an inverse of each other?

There are two different processes he's describing here, not two graphs of the same process. The first describes unemployment as a function of inflation - the second describes inflation as a function of unemployment.

Why are you under the impression that these two functions are just each other's inverse? How does that make sense?

So, if the Fed says, "We are going to aim for 2 percent inflation," the market is going to say, "Sorry, but that will only raise aggregate demand enough to get you to 6 percent unemployment, which won't get you to 2 percent inflation (because of the aforementioned Phillips Curve). Therefore, we don't believe you, and so we won't let inflation go up at all."

Did no one else notice that this is circular?

And seriously, the Phillips Curve? The greatest correlation/causation fallacy in all of 20th century economics? I really thought we had put that out to pasture.

"Look, let's not be daft. Krugman assumes a set of conditions that work out to 5% unemployment in the first picture and a set of conditions that work out to 6% unemployment in the second picture."

You are wrong about the second picture; in the second picture the unemployment is the exogenous variable, not the explained variable - then, in the second picture he is not presenting a set of conditions that work out to 6% unemployment: he is not saying that 1% of inflation will create an unemployment of 6%; he is saying the opposite: that 6% of unemployment will create an inflation of 1%

RE: "That's fine, but given that both of these pictures depict a relationship between inflation and employment, then all Krugman has told us is that he's changed his assumptions."

You really need to read these comments before posting. Two variables - two different relationships. This really should not be that hard. One describes the determination of inflation, the other describes the determination of unemployment. You're welcome to dispute the nature of the realtionships, but this point you keep harping on that it's somehow internally inconsistent is absurd.

RP Long - think of a simply supply and demand model. Both the supply curve and the demand curve depict a relationship between quantity and price. But just because they're not the same relationship, you don't say that people "change their assumptions" when talking about quantity and prices.

The power of supply and demand is that we KNOW the supply relationship between p and q has to hold true and we KNOW the demand relationship between p and q has to hold true, and there's only one point where they both hold true at the same time.

That's all Krugman is doing here. Two distinct processes in two unknowns gets you at least one solution. It may not be a stable solution - there may be multiple solutions - but as I said above, this is pretty much middle school math so I wouldn't go around being incredulous at how a Nobel laureate graduated high school.

Has it occurred to either of you that simply reversing the causality relationship between inflation and employment is itself a change in one's assumptions? Either inflation causes employment or employment causes inflation - it can't be both at the same time under the same set of assumptions (unless we're leaving something out).

Now, that parenthetical statement I just made is the crux of the whole issue. Krugman thinks he can dance around this by conflating the issue with contradictory assumptions. But this is a game. As I said above, you cannot provide any insight into the economy by simply reversing the causal relationship between two variables in mid-explanation.

Scott Sumner would call this "the fallacy of reasoning from a price change" (in this case, a change in the price of currency). I, on the other hand, would simply call it unscientific.

And it is because is a "positive feedback" system that have a "no man's-land": systems with positive feedback can have two (or more) distant possible equilibrium points, but with an unstable intermediate area between these possible equilibrium

You can't assume both relationships at the same time to explain the same phenomenon. Don't forget - these are economic models, not actual economies.

Traffic light variation can cause higher traffic volumes, and higher traffic volumes can cause traffic light variation. But when you assume both relationships to explain a traffic jam, then you've effectively said nothing.

"Traffic light variation can cause higher traffic volumes, and higher traffic volumes can cause traffic light variation. But when you assume both relationships to explain a traffic jam, then you've effectively said nothing.

See what I'm saying yet?"

No, because if I say that, I am saying something: that traffic light variation and traffic volumes have a mutual reinforcement relation, with the eventual possibility of having two stable equilibrium - one with low traffic volume, and other with high traffic volume.

[the example of "higher traffic volumes can cause traffic light variation" seems a bit irrealistic, but we can easily imagine a more realistic example]

By justifying a model with a theory, rather than justifying a theory with a model, you've effectively proved my point.

To be sure, I'm not objecting to Krugman out of ignorance of Keynesian theory. I'm objecting based on my criticism of it.

"There is a feedback loop between employment and inflation" is not an explanation of anything, it is a dance. One of my old professors used to say, "By saying everything, you have said nothing."

Either there is a determinable cause-effect relationship between employment and inflation, or something else is going on. By claiming that the causality can go either way at any time - and even worse, by changing which causality relationship you're talking about in mid-explanation - you are essentially justifying any and every possible explanation that involves a relationship between those two.

Having noted that, we simply have no choice but to reject the explanation in favor of one with more descriptive power. When you think about it, there is no real reason why higher levels of employment would increase the total supply of currency in the first place. Whereas, inflation can only cause greater levels of employment if there is malinvestment going on.

Either there is a determinable cause-effect relationship between employment and inflation, or something else is going on. By claiming that the causality can go either way at any time - and even worse, by changing which causality relationship you're talking about in mid-explanation - you are essentially justifying any and every possible explanation that involves a relationship between those two.

There is a determinable cause-and-effect relationship (presented in a simplified way here, but that's presumably not the major issue). Both are causes and both are effects - it's an endogenous process. It's not simply that the causality "can go either way at any time" - it's that it goes BOTH ways ALL the time. And nobody is changing which causality relationship we're talking about - we have been talking about both relationships throughout.

We have two things we're trying to understand here - inflation and unemployment. The only way to grapple with it is to explain both as independent processes and put both of those explanations together to see what the total system will settle out to. That's all he's doing. What you advise - talking about one process at a time or even insisting there can only be one relationship between two variables - is not only inaccurate, it's completely unhelpful in thinking about the relationship between inflation and unemployment. Krugman may ultimately be wrong - that's something of an empirical question - but he is approaching the question in the right way.

"There is a feedback loop between employment and inflation" is not an explanation of anything, it is a dance. One of my old professors used to say, "By saying everything, you have said nothing."

I don't think you quite understand what your professor was trying to teach you.

You are the one that wants to try to explain what happens with two unknowns using only one relationship between the two variables. There are two possible outcomes of that approach:

1. If that understanding of the relationship between those two variables is correct, then you're doing precisely what your professor advised you against - not homing in on any sort of unique (or even finite) solution and therefore not saying anything.

2. If that understanding of the relationship is wrong, then not only are you saying everything and therefore saying nothing (because you have no equilibrium conditions to think about) - you are actually wrong as well because you haven't taken into account all the causal factors involved.

Miguel, Krugman, and I may be wrong too if our assumptions are wrong - but one thing we are most definitely not guilty of is "saying everything and therefore saying nothing".

Daniel, I appreciate your taking the time to discuss this with me. Unfortunatley, we seem to be at different stages of the debate. You seem to think that if you just explain Krugman's faulty model better, I'll "understand." In reality I understand full well.

Unfortunately, there is very little difference between what you and I are saying. You say the cause and effect relationship goes both ways all the time; I say that proclaiming this to be true is bad science.

The problem with Keynesianism is that it is quasi-religion. It's like the holy trinity: If god can be a man and a god and a feeling, depending on how god feels, then you can theoretically explain anything by changing god's form to fit the situation. Krugman is doing this, too: when it becomes inconvenient to suggest that inflation causes employment, then he reverses the causality. (After all, the relationship goes both ways! God is both a man and a god!)

Those who buy into this explanation of the macroeconomy are those who are good at using the language. The true cause-effect relationships will continue to elude them because when one falls short, they replace it with its reverse. It is a handy intellectual escape for a bad macro model.

At least in religion we aren't trying to explain anything about the physical universe, only our ethical and metaphysical systems. Economics has no such luxury - every theory must be consistent, coherent, and enlightening or else we must discard it. Failing to do so is simply bad science.

The Phillips Curve is old and silly by modern standards. The objections I have outlined above are not the least of its problems, they are merely the initial a priori problems. I have focused on these problems here because that's where my interest lies. The other problems are well documented elsewhere.

RP Long -
When you just assert that two things can't cause each other and don't explain why you think that, there's no real way to respond to that. When you just call Keynesianism quasi-religion without disputing a single point, there's no way to respond to that (that's a little out of left field anyway - we're not really discussing "Keynesianism" here).

Krugman is doing this, too: when it becomes inconvenient to suggest that inflation causes employment, then he reverses the causality.

No causality is "reversed" at all, RP Long. This is why it seems like you're not understanding what's being said. Causality is never reversed it always runs both ways. A person is smart because he received an education, but he received an education because he is smart (and knew it was good for him). These are very basic simultaneously determined systems. There is no "reversal" here to speak of.

If you still think that this is an issue of reversing causality or replacing one relationship with the other then you have no idea what you're talking about.

RPLong, I have some doubts in understanding what is exactly the nature of your objection to Krugman's model. More exacttly, you are saying that the model is

a) logical inconsistent;

or

b) impossible to empirically test?

These are two different criticism - a model can be logical coherent (in the sense of being consistent with the premises) but being impossible to test; and can be logically incoeherent but possible to test.

In your first comments, I had the impression that you were making the criticism a), but perhaps I misunderstud and you are really making the criticism b) (it is the impression that I have from your last comments).

If I understand the interpretation in this post, I believe it is the correct one, but I don't see anything strange about the model Krugman is using. It is the standard Keynesian model. Krugman's first curve is the standard IS curve, but with the nominal interest rate constrained to zero, so that the real interest rate depends on the expected inflation rate. The second curve is the standard Phillips curve, which determines the actual inflation rate. The equilibrium condition is that the actual inflation rate equals the expected inflation rate. There are two equilibria that meet this condition. (If you relax the zero nominal interest rate assumption, then there is also a continuum of other equilibria that involve higher nominal interest rates and higher inflation rates.)

If this model seems strange, that's probably because you are used to a world without a binding zero interest rate constraint. But the word "discontinuity" is misleading. It's really a matter of having two equilibria. The continuity that we experience with macro policy under normal conditions is a result of our continuous control of the nominal interest rate. When we lose that control and are obliged to accept one specific nominal interest rate (zero), then we lose the continuity of possibilities. Usually, for any given nominal interest rate, we think (perhaps wrongly) that there is only one equilibrium, and we say that the interest rate "determines" the equilibrium. It turns out there are actually two equilibria in this case -- and it happens that they are not right next to each other, so there is a "discontinuity." But there's not really anything "continuous" about having a single equilibrium either.

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